Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(1,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.993.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.480031\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.519969 | −0.300204 | −0.150102 | − | 0.988670i | \(-0.547960\pi\) | ||||
−0.150102 | + | 0.988670i | \(0.547960\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.519969 | 0.212277 | ||||||||
\(7\) | −4.76957 | −1.80273 | −0.901364 | − | 0.433062i | \(-0.857433\pi\) | ||||
−0.901364 | + | 0.433062i | \(0.857433\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.72963 | −0.909877 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.960061 | 0.289469 | 0.144735 | − | 0.989471i | \(-0.453767\pi\) | ||||
0.144735 | + | 0.989471i | \(0.453767\pi\) | |||||||
\(12\) | −0.519969 | −0.150102 | ||||||||
\(13\) | −2.24960 | −0.623927 | −0.311964 | − | 0.950094i | \(-0.600987\pi\) | ||||
−0.311964 | + | 0.950094i | \(0.600987\pi\) | |||||||
\(14\) | 4.76957 | 1.27472 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.249601 | 0.0605372 | 0.0302686 | − | 0.999542i | \(-0.490364\pi\) | ||||
0.0302686 | + | 0.999542i | \(0.490364\pi\) | |||||||
\(18\) | 2.72963 | 0.643380 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.48003 | 0.541187 | ||||||||
\(22\) | −0.960061 | −0.204686 | ||||||||
\(23\) | 9.01917 | 1.88063 | 0.940314 | − | 0.340309i | \(-0.110532\pi\) | ||||
0.940314 | + | 0.340309i | \(0.110532\pi\) | |||||||
\(24\) | 0.519969 | 0.106138 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.24960 | 0.441183 | ||||||||
\(27\) | 2.97923 | 0.573354 | ||||||||
\(28\) | −4.76957 | −0.901364 | ||||||||
\(29\) | 6.24960 | 1.16052 | 0.580261 | − | 0.814431i | \(-0.302951\pi\) | ||||
0.580261 | + | 0.814431i | \(0.302951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96006 | 0.531643 | 0.265821 | − | 0.964022i | \(-0.414357\pi\) | ||||
0.265821 | + | 0.964022i | \(0.414357\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.499202 | −0.0869000 | ||||||||
\(34\) | −0.249601 | −0.0428063 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.72963 | −0.454939 | ||||||||
\(37\) | 0.0399387 | 0.00656589 | 0.00328294 | − | 0.999995i | \(-0.498955\pi\) | ||||
0.00328294 | + | 0.999995i | \(0.498955\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 1.16972 | 0.187306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −2.48003 | −0.382677 | ||||||||
\(43\) | 4.96006 | 0.756402 | 0.378201 | − | 0.925723i | \(-0.376543\pi\) | ||||
0.378201 | + | 0.925723i | \(0.376543\pi\) | |||||||
\(44\) | 0.960061 | 0.144735 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.01917 | −1.32980 | ||||||||
\(47\) | −9.49920 | −1.38560 | −0.692801 | − | 0.721129i | \(-0.743623\pi\) | ||||
−0.692801 | + | 0.721129i | \(0.743623\pi\) | |||||||
\(48\) | −0.519969 | −0.0750511 | ||||||||
\(49\) | 15.7488 | 2.24983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.129785 | −0.0181735 | ||||||||
\(52\) | −2.24960 | −0.311964 | ||||||||
\(53\) | 6.84945 | 0.940844 | 0.470422 | − | 0.882442i | \(-0.344102\pi\) | ||||
0.470422 | + | 0.882442i | \(0.344102\pi\) | |||||||
\(54\) | −2.97923 | −0.405422 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.76957 | 0.637361 | ||||||||
\(57\) | −0.519969 | −0.0688716 | ||||||||
\(58\) | −6.24960 | −0.820613 | ||||||||
\(59\) | −14.5583 | −1.89533 | −0.947665 | − | 0.319265i | \(-0.896564\pi\) | ||||
−0.947665 | + | 0.319265i | \(0.896564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.53914 | 0.965288 | 0.482644 | − | 0.875817i | \(-0.339676\pi\) | ||||
0.482644 | + | 0.875817i | \(0.339676\pi\) | |||||||
\(62\) | −2.96006 | −0.375928 | ||||||||
\(63\) | 13.0192 | 1.64026 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.499202 | 0.0614476 | ||||||||
\(67\) | −5.72963 | −0.699986 | −0.349993 | − | 0.936752i | \(-0.613816\pi\) | ||||
−0.349993 | + | 0.936752i | \(0.613816\pi\) | |||||||
\(68\) | 0.249601 | 0.0302686 | ||||||||
\(69\) | −4.68969 | −0.564573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.61902 | −1.14157 | −0.570784 | − | 0.821100i | \(-0.693361\pi\) | ||||
−0.570784 | + | 0.821100i | \(0.693361\pi\) | |||||||
\(72\) | 2.72963 | 0.321690 | ||||||||
\(73\) | 12.0591 | 1.41141 | 0.705706 | − | 0.708505i | \(-0.250630\pi\) | ||||
0.705706 | + | 0.708505i | \(0.250630\pi\) | |||||||
\(74\) | −0.0399387 | −0.00464278 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −4.57908 | −0.521835 | ||||||||
\(78\) | −1.16972 | −0.132445 | ||||||||
\(79\) | 6.07988 | 0.684040 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.63979 | 0.737754 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.45926 | −0.818761 | −0.409380 | − | 0.912364i | \(-0.634255\pi\) | ||||
−0.409380 | + | 0.912364i | \(0.634255\pi\) | |||||||
\(84\) | 2.48003 | 0.270594 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.96006 | −0.534857 | ||||||||
\(87\) | −3.24960 | −0.348394 | ||||||||
\(88\) | −0.960061 | −0.102343 | ||||||||
\(89\) | 4.07988 | 0.432466 | 0.216233 | − | 0.976342i | \(-0.430623\pi\) | ||||
0.216233 | + | 0.976342i | \(0.430623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.7296 | 1.12477 | ||||||||
\(92\) | 9.01917 | 0.940314 | ||||||||
\(93\) | −1.53914 | −0.159602 | ||||||||
\(94\) | 9.49920 | 0.979768 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.519969 | 0.0530692 | ||||||||
\(97\) | 18.4193 | 1.87020 | 0.935100 | − | 0.354385i | \(-0.115310\pi\) | ||||
0.935100 | + | 0.354385i | \(0.115310\pi\) | |||||||
\(98\) | −15.7488 | −1.59087 | ||||||||
\(99\) | −2.62061 | −0.263382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.53914 | 0.551165 | 0.275583 | − | 0.961277i | \(-0.411129\pi\) | ||||
0.275583 | + | 0.961277i | \(0.411129\pi\) | |||||||
\(102\) | 0.129785 | 0.0128506 | ||||||||
\(103\) | −6.57908 | −0.648256 | −0.324128 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324128 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(104\) | 2.24960 | 0.220592 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.84945 | −0.665277 | ||||||||
\(107\) | 14.9086 | 1.44126 | 0.720632 | − | 0.693317i | \(-0.243852\pi\) | ||||
0.720632 | + | 0.693317i | \(0.243852\pi\) | |||||||
\(108\) | 2.97923 | 0.286677 | ||||||||
\(109\) | 4.76957 | 0.456842 | 0.228421 | − | 0.973562i | \(-0.426644\pi\) | ||||
0.228421 | + | 0.973562i | \(0.426644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0207669 | −0.00197111 | ||||||||
\(112\) | −4.76957 | −0.450682 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0.519969 | 0.0486996 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.24960 | 0.580261 | ||||||||
\(117\) | 6.14058 | 0.567697 | ||||||||
\(118\) | 14.5583 | 1.34020 | ||||||||
\(119\) | −1.19049 | −0.109132 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0783 | −0.916207 | ||||||||
\(122\) | −7.53914 | −0.682562 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.96006 | 0.265821 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.0192 | −1.15984 | ||||||||
\(127\) | 17.9585 | 1.59356 | 0.796778 | − | 0.604272i | \(-0.206536\pi\) | ||||
0.796778 | + | 0.604272i | \(0.206536\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.57908 | −0.227075 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.96006 | −0.608103 | −0.304052 | − | 0.952656i | \(-0.598340\pi\) | ||||
−0.304052 | + | 0.952656i | \(0.598340\pi\) | |||||||
\(132\) | −0.499202 | −0.0434500 | ||||||||
\(133\) | −4.76957 | −0.413574 | ||||||||
\(134\) | 5.72963 | 0.494965 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.249601 | −0.0214031 | ||||||||
\(137\) | 7.80951 | 0.667211 | 0.333606 | − | 0.942713i | \(-0.391735\pi\) | ||||
0.333606 | + | 0.942713i | \(0.391735\pi\) | |||||||
\(138\) | 4.68969 | 0.399213 | ||||||||
\(139\) | −16.0383 | −1.36035 | −0.680177 | − | 0.733048i | \(-0.738097\pi\) | ||||
−0.680177 | + | 0.733048i | \(0.738097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.93929 | 0.415964 | ||||||||
\(142\) | 9.61902 | 0.807210 | ||||||||
\(143\) | −2.15975 | −0.180608 | ||||||||
\(144\) | −2.72963 | −0.227469 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0591 | −0.998019 | ||||||||
\(147\) | −8.18890 | −0.675409 | ||||||||
\(148\) | 0.0399387 | 0.00328294 | ||||||||
\(149\) | −8.41932 | −0.689738 | −0.344869 | − | 0.938651i | \(-0.612077\pi\) | ||||
−0.344869 | + | 0.938651i | \(0.612077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −0.681319 | −0.0550814 | ||||||||
\(154\) | 4.57908 | 0.368993 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.16972 | 0.0936529 | ||||||||
\(157\) | 4.96006 | 0.395856 | 0.197928 | − | 0.980217i | \(-0.436579\pi\) | ||||
0.197928 | + | 0.980217i | \(0.436579\pi\) | |||||||
\(158\) | −6.07988 | −0.483689 | ||||||||
\(159\) | −3.56150 | −0.282446 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −43.0176 | −3.39026 | ||||||||
\(162\) | −6.63979 | −0.521671 | ||||||||
\(163\) | −21.4593 | −1.68082 | −0.840410 | − | 0.541952i | \(-0.817686\pi\) | ||||
−0.840410 | + | 0.541952i | \(0.817686\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.45926 | 0.578951 | ||||||||
\(167\) | −11.0399 | −0.854296 | −0.427148 | − | 0.904182i | \(-0.640482\pi\) | ||||
−0.427148 | + | 0.904182i | \(0.640482\pi\) | |||||||
\(168\) | −2.48003 | −0.191339 | ||||||||
\(169\) | −7.93929 | −0.610715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.72963 | −0.208740 | ||||||||
\(172\) | 4.96006 | 0.378201 | ||||||||
\(173\) | 16.9585 | 1.28933 | 0.644664 | − | 0.764466i | \(-0.276997\pi\) | ||||
0.644664 | + | 0.764466i | \(0.276997\pi\) | |||||||
\(174\) | 3.24960 | 0.246352 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.960061 | 0.0723673 | ||||||||
\(177\) | 7.56988 | 0.568987 | ||||||||
\(178\) | −4.07988 | −0.305800 | ||||||||
\(179\) | 2.53914 | 0.189784 | 0.0948922 | − | 0.995488i | \(-0.469749\pi\) | ||||
0.0948922 | + | 0.995488i | \(0.469749\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.88018 | −0.288412 | −0.144206 | − | 0.989548i | \(-0.546063\pi\) | ||||
−0.144206 | + | 0.989548i | \(0.546063\pi\) | |||||||
\(182\) | −10.7296 | −0.795333 | ||||||||
\(183\) | −3.92012 | −0.289784 | ||||||||
\(184\) | −9.01917 | −0.664902 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.53914 | 0.112855 | ||||||||
\(187\) | 0.239632 | 0.0175237 | ||||||||
\(188\) | −9.49920 | −0.692801 | ||||||||
\(189\) | −14.2097 | −1.03360 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.05911 | 0.148992 | 0.0744960 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744960 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(192\) | −0.519969 | −0.0375256 | ||||||||
\(193\) | −8.46086 | −0.609026 | −0.304513 | − | 0.952508i | \(-0.598494\pi\) | ||||
−0.304513 | + | 0.952508i | \(0.598494\pi\) | |||||||
\(194\) | −18.4193 | −1.32243 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7488 | 1.12491 | ||||||||
\(197\) | 13.9201 | 0.991768 | 0.495884 | − | 0.868389i | \(-0.334844\pi\) | ||||
0.495884 | + | 0.868389i | \(0.334844\pi\) | |||||||
\(198\) | 2.62061 | 0.186239 | ||||||||
\(199\) | −9.15055 | −0.648665 | −0.324333 | − | 0.945943i | \(-0.605140\pi\) | ||||
−0.324333 | + | 0.945943i | \(0.605140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.97923 | 0.210139 | ||||||||
\(202\) | −5.53914 | −0.389733 | ||||||||
\(203\) | −29.8079 | −2.09211 | ||||||||
\(204\) | −0.129785 | −0.00908677 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.57908 | 0.458386 | ||||||||
\(207\) | −24.6190 | −1.71114 | ||||||||
\(208\) | −2.24960 | −0.155982 | ||||||||
\(209\) | 0.960061 | 0.0664088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5200 | 1.13728 | 0.568641 | − | 0.822586i | \(-0.307469\pi\) | ||||
0.568641 | + | 0.822586i | \(0.307469\pi\) | |||||||
\(212\) | 6.84945 | 0.470422 | ||||||||
\(213\) | 5.00160 | 0.342704 | ||||||||
\(214\) | −14.9086 | −1.01913 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.97923 | −0.202711 | ||||||||
\(217\) | −14.1182 | −0.958407 | ||||||||
\(218\) | −4.76957 | −0.323036 | ||||||||
\(219\) | −6.27037 | −0.423712 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.561503 | −0.0377708 | ||||||||
\(222\) | 0.0207669 | 0.00139378 | ||||||||
\(223\) | 9.03994 | 0.605359 | 0.302680 | − | 0.953092i | \(-0.402119\pi\) | ||||
0.302680 | + | 0.953092i | \(0.402119\pi\) | |||||||
\(224\) | 4.76957 | 0.318680 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 0.350246 | 0.0232466 | 0.0116233 | − | 0.999932i | \(-0.496300\pi\) | ||||
0.0116233 | + | 0.999932i | \(0.496300\pi\) | |||||||
\(228\) | −0.519969 | −0.0344358 | ||||||||
\(229\) | −8.07988 | −0.533933 | −0.266967 | − | 0.963706i | \(-0.586021\pi\) | ||||
−0.266967 | + | 0.963706i | \(0.586021\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.38098 | 0.156657 | ||||||||
\(232\) | −6.24960 | −0.410306 | ||||||||
\(233\) | −4.92012 | −0.322328 | −0.161164 | − | 0.986928i | \(-0.551525\pi\) | ||||
−0.161164 | + | 0.986928i | \(0.551525\pi\) | |||||||
\(234\) | −6.14058 | −0.401422 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.5583 | −0.947665 | ||||||||
\(237\) | −3.16135 | −0.205352 | ||||||||
\(238\) | 1.19049 | 0.0771680 | ||||||||
\(239\) | 2.98083 | 0.192814 | 0.0964069 | − | 0.995342i | \(-0.469265\pi\) | ||||
0.0964069 | + | 0.995342i | \(0.469265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0383 | 1.29078 | 0.645392 | − | 0.763852i | \(-0.276694\pi\) | ||||
0.645392 | + | 0.763852i | \(0.276694\pi\) | |||||||
\(242\) | 10.0783 | 0.647857 | ||||||||
\(243\) | −12.3902 | −0.794831 | ||||||||
\(244\) | 7.53914 | 0.482644 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24960 | −0.143139 | ||||||||
\(248\) | −2.96006 | −0.187964 | ||||||||
\(249\) | 3.87859 | 0.245796 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.8802 | −0.939229 | −0.469614 | − | 0.882872i | \(-0.655607\pi\) | ||||
−0.469614 | + | 0.882872i | \(0.655607\pi\) | |||||||
\(252\) | 13.0192 | 0.820131 | ||||||||
\(253\) | 8.65896 | 0.544384 | ||||||||
\(254\) | −17.9585 | −1.12681 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.0399 | −0.688652 | −0.344326 | − | 0.938850i | \(-0.611893\pi\) | ||||
−0.344326 | + | 0.938850i | \(0.611893\pi\) | |||||||
\(258\) | 2.57908 | 0.160567 | ||||||||
\(259\) | −0.190491 | −0.0118365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.0591 | −1.05593 | ||||||||
\(262\) | 6.96006 | 0.429994 | ||||||||
\(263\) | −3.84025 | −0.236800 | −0.118400 | − | 0.992966i | \(-0.537776\pi\) | ||||
−0.118400 | + | 0.992966i | \(0.537776\pi\) | |||||||
\(264\) | 0.499202 | 0.0307238 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.76957 | 0.292441 | ||||||||
\(267\) | −2.12141 | −0.129828 | ||||||||
\(268\) | −5.72963 | −0.349993 | ||||||||
\(269\) | 23.1981 | 1.41441 | 0.707207 | − | 0.707007i | \(-0.249955\pi\) | ||||
0.707207 | + | 0.707007i | \(0.249955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9792 | 1.45663 | 0.728317 | − | 0.685240i | \(-0.240303\pi\) | ||||
0.728317 | + | 0.685240i | \(0.240303\pi\) | |||||||
\(272\) | 0.249601 | 0.0151343 | ||||||||
\(273\) | −5.57908 | −0.337661 | ||||||||
\(274\) | −7.80951 | −0.471790 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.68969 | −0.282286 | ||||||||
\(277\) | 24.6590 | 1.48161 | 0.740807 | − | 0.671718i | \(-0.234444\pi\) | ||||
0.740807 | + | 0.671718i | \(0.234444\pi\) | |||||||
\(278\) | 16.0383 | 0.961916 | ||||||||
\(279\) | −8.07988 | −0.483730 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9984 | −1.13335 | −0.566675 | − | 0.823941i | \(-0.691770\pi\) | ||||
−0.566675 | + | 0.823941i | \(0.691770\pi\) | |||||||
\(282\) | −4.93929 | −0.294131 | ||||||||
\(283\) | 29.0367 | 1.72606 | 0.863028 | − | 0.505156i | \(-0.168565\pi\) | ||||
0.863028 | + | 0.505156i | \(0.168565\pi\) | |||||||
\(284\) | −9.61902 | −0.570784 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.15975 | 0.127709 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.72963 | 0.160845 | ||||||||
\(289\) | −16.9377 | −0.996335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.57748 | −0.561442 | ||||||||
\(292\) | 12.0591 | 0.705706 | ||||||||
\(293\) | 6.24960 | 0.365106 | 0.182553 | − | 0.983196i | \(-0.441564\pi\) | ||||
0.182553 | + | 0.983196i | \(0.441564\pi\) | |||||||
\(294\) | 8.18890 | 0.477586 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.0399387 | −0.00232139 | ||||||||
\(297\) | 2.86025 | 0.165968 | ||||||||
\(298\) | 8.41932 | 0.487718 | ||||||||
\(299\) | −20.2895 | −1.17337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.6574 | −1.36359 | ||||||||
\(302\) | −20.0000 | −1.15087 | ||||||||
\(303\) | −2.88018 | −0.165462 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.681319 | 0.0389484 | ||||||||
\(307\) | 12.5391 | 0.715647 | 0.357823 | − | 0.933789i | \(-0.383519\pi\) | ||||
0.357823 | + | 0.933789i | \(0.383519\pi\) | |||||||
\(308\) | −4.57908 | −0.260917 | ||||||||
\(309\) | 3.42092 | 0.194609 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.84785 | 0.445011 | 0.222505 | − | 0.974931i | \(-0.428576\pi\) | ||||
0.222505 | + | 0.974931i | \(0.428576\pi\) | |||||||
\(312\) | −1.16972 | −0.0662226 | ||||||||
\(313\) | 10.9884 | 0.621103 | 0.310552 | − | 0.950557i | \(-0.399486\pi\) | ||||
0.310552 | + | 0.950557i | \(0.399486\pi\) | |||||||
\(314\) | −4.96006 | −0.279912 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.07988 | 0.342020 | ||||||||
\(317\) | −21.5567 | −1.21075 | −0.605373 | − | 0.795942i | \(-0.706976\pi\) | ||||
−0.605373 | + | 0.795942i | \(0.706976\pi\) | |||||||
\(318\) | 3.56150 | 0.199719 | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.75199 | −0.432674 | ||||||||
\(322\) | 43.0176 | 2.39728 | ||||||||
\(323\) | 0.249601 | 0.0138882 | ||||||||
\(324\) | 6.63979 | 0.368877 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.4593 | 1.18852 | ||||||||
\(327\) | −2.48003 | −0.137146 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 45.3071 | 2.49786 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.4876 | 1.84065 | 0.920324 | − | 0.391158i | \(-0.127925\pi\) | ||||
0.920324 | + | 0.391158i | \(0.127925\pi\) | |||||||
\(332\) | −7.45926 | −0.409380 | ||||||||
\(333\) | −0.109018 | −0.00597415 | ||||||||
\(334\) | 11.0399 | 0.604079 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.48003 | 0.135297 | ||||||||
\(337\) | 5.69890 | 0.310439 | 0.155219 | − | 0.987880i | \(-0.450392\pi\) | ||||
0.155219 | + | 0.987880i | \(0.450392\pi\) | |||||||
\(338\) | 7.93929 | 0.431841 | ||||||||
\(339\) | −3.11982 | −0.169445 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.84184 | 0.153894 | ||||||||
\(342\) | 2.72963 | 0.147602 | ||||||||
\(343\) | −41.7280 | −2.25310 | ||||||||
\(344\) | −4.96006 | −0.267429 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.9585 | −0.911693 | ||||||||
\(347\) | −0.239632 | −0.0128641 | −0.00643207 | − | 0.999979i | \(-0.502047\pi\) | ||||
−0.00643207 | + | 0.999979i | \(0.502047\pi\) | |||||||
\(348\) | −3.24960 | −0.174197 | ||||||||
\(349\) | −17.2380 | −0.922731 | −0.461365 | − | 0.887210i | \(-0.652640\pi\) | ||||
−0.461365 | + | 0.887210i | \(0.652640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.70209 | −0.357731 | ||||||||
\(352\) | −0.960061 | −0.0511714 | ||||||||
\(353\) | −34.7280 | −1.84839 | −0.924193 | − | 0.381925i | \(-0.875261\pi\) | ||||
−0.924193 | + | 0.381925i | \(0.875261\pi\) | |||||||
\(354\) | −7.56988 | −0.402334 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.07988 | 0.216233 | ||||||||
\(357\) | 0.619019 | 0.0327619 | ||||||||
\(358\) | −2.53914 | −0.134198 | ||||||||
\(359\) | 26.6689 | 1.40753 | 0.703766 | − | 0.710432i | \(-0.251500\pi\) | ||||
0.703766 | + | 0.710432i | \(0.251500\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 3.88018 | 0.203938 | ||||||||
\(363\) | 5.24040 | 0.275050 | ||||||||
\(364\) | 10.7296 | 0.562386 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.92012 | 0.204908 | ||||||||
\(367\) | −15.2380 | −0.795419 | −0.397710 | − | 0.917511i | \(-0.630195\pi\) | ||||
−0.397710 | + | 0.917511i | \(0.630195\pi\) | |||||||
\(368\) | 9.01917 | 0.470157 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.6689 | −1.69609 | ||||||||
\(372\) | −1.53914 | −0.0798008 | ||||||||
\(373\) | −26.6382 | −1.37927 | −0.689637 | − | 0.724156i | \(-0.742230\pi\) | ||||
−0.689637 | + | 0.724156i | \(0.742230\pi\) | |||||||
\(374\) | −0.239632 | −0.0123911 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.49920 | 0.489884 | ||||||||
\(377\) | −14.0591 | −0.724081 | ||||||||
\(378\) | 14.2097 | 0.730866 | ||||||||
\(379\) | 11.9693 | 0.614820 | 0.307410 | − | 0.951577i | \(-0.400538\pi\) | ||||
0.307410 | + | 0.951577i | \(0.400538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.33785 | −0.478393 | ||||||||
\(382\) | −2.05911 | −0.105353 | ||||||||
\(383\) | −9.84025 | −0.502813 | −0.251407 | − | 0.967882i | \(-0.580893\pi\) | ||||
−0.251407 | + | 0.967882i | \(0.580893\pi\) | |||||||
\(384\) | 0.519969 | 0.0265346 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.46086 | 0.430646 | ||||||||
\(387\) | −13.5391 | −0.688233 | ||||||||
\(388\) | 18.4193 | 0.935100 | ||||||||
\(389\) | −8.65896 | −0.439027 | −0.219513 | − | 0.975610i | \(-0.570447\pi\) | ||||
−0.219513 | + | 0.975610i | \(0.570447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.25120 | 0.113848 | ||||||||
\(392\) | −15.7488 | −0.795435 | ||||||||
\(393\) | 3.61902 | 0.182555 | ||||||||
\(394\) | −13.9201 | −0.701286 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.62061 | −0.131691 | ||||||||
\(397\) | 28.9984 | 1.45539 | 0.727694 | − | 0.685902i | \(-0.240592\pi\) | ||||
0.727694 | + | 0.685902i | \(0.240592\pi\) | |||||||
\(398\) | 9.15055 | 0.458676 | ||||||||
\(399\) | 2.48003 | 0.124157 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6174 | 1.12946 | 0.564730 | − | 0.825276i | \(-0.308980\pi\) | ||||
0.564730 | + | 0.825276i | \(0.308980\pi\) | |||||||
\(402\) | −2.97923 | −0.148591 | ||||||||
\(403\) | −6.65896 | −0.331706 | ||||||||
\(404\) | 5.53914 | 0.275583 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 29.8079 | 1.47934 | ||||||||
\(407\) | 0.0383436 | 0.00190062 | ||||||||
\(408\) | 0.129785 | 0.00642531 | ||||||||
\(409\) | 5.34104 | 0.264098 | 0.132049 | − | 0.991243i | \(-0.457844\pi\) | ||||
0.132049 | + | 0.991243i | \(0.457844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.06071 | −0.200300 | ||||||||
\(412\) | −6.57908 | −0.324128 | ||||||||
\(413\) | 69.4369 | 3.41677 | ||||||||
\(414\) | 24.6190 | 1.20996 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.24960 | 0.110296 | ||||||||
\(417\) | 8.33945 | 0.408384 | ||||||||
\(418\) | −0.960061 | −0.0469581 | ||||||||
\(419\) | −22.1566 | −1.08242 | −0.541210 | − | 0.840888i | \(-0.682033\pi\) | ||||
−0.541210 | + | 0.840888i | \(0.682033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.2787 | 1.42696 | 0.713479 | − | 0.700676i | \(-0.247118\pi\) | ||||
0.713479 | + | 0.700676i | \(0.247118\pi\) | |||||||
\(422\) | −16.5200 | −0.804180 | ||||||||
\(423\) | 25.9293 | 1.26073 | ||||||||
\(424\) | −6.84945 | −0.332639 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.00160 | −0.242328 | ||||||||
\(427\) | −35.9585 | −1.74015 | ||||||||
\(428\) | 14.9086 | 0.720632 | ||||||||
\(429\) | 1.12301 | 0.0542193 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.3794 | 1.02981 | 0.514904 | − | 0.857248i | \(-0.327827\pi\) | ||||
0.514904 | + | 0.857248i | \(0.327827\pi\) | |||||||
\(432\) | 2.97923 | 0.143338 | ||||||||
\(433\) | −36.1182 | −1.73573 | −0.867865 | − | 0.496799i | \(-0.834509\pi\) | ||||
−0.867865 | + | 0.496799i | \(0.834509\pi\) | |||||||
\(434\) | 14.1182 | 0.677696 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.76957 | 0.228421 | ||||||||
\(437\) | 9.01917 | 0.431445 | ||||||||
\(438\) | 6.27037 | 0.299610 | ||||||||
\(439\) | 20.9984 | 1.00220 | 0.501100 | − | 0.865390i | \(-0.332929\pi\) | ||||
0.501100 | + | 0.865390i | \(0.332929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.9884 | −2.04707 | ||||||||
\(442\) | 0.561503 | 0.0267080 | ||||||||
\(443\) | −31.4976 | −1.49650 | −0.748248 | − | 0.663419i | \(-0.769105\pi\) | ||||
−0.748248 | + | 0.663419i | \(0.769105\pi\) | |||||||
\(444\) | −0.0207669 | −0.000985555 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.03994 | −0.428054 | ||||||||
\(447\) | 4.37779 | 0.207062 | ||||||||
\(448\) | −4.76957 | −0.225341 | ||||||||
\(449\) | 18.9601 | 0.894781 | 0.447390 | − | 0.894339i | \(-0.352353\pi\) | ||||
0.447390 | + | 0.894339i | \(0.352353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | −10.3994 | −0.488606 | ||||||||
\(454\) | −0.350246 | −0.0164378 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.519969 | 0.0243498 | ||||||||
\(457\) | −6.32948 | −0.296081 | −0.148040 | − | 0.988981i | \(-0.547297\pi\) | ||||
−0.148040 | + | 0.988981i | \(0.547297\pi\) | |||||||
\(458\) | 8.07988 | 0.377548 | ||||||||
\(459\) | 0.743620 | 0.0347092 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.49920 | −0.302698 | −0.151349 | − | 0.988480i | \(-0.548362\pi\) | ||||
−0.151349 | + | 0.988480i | \(0.548362\pi\) | |||||||
\(462\) | −2.38098 | −0.110773 | ||||||||
\(463\) | 28.4177 | 1.32068 | 0.660342 | − | 0.750965i | \(-0.270411\pi\) | ||||
0.660342 | + | 0.750965i | \(0.270411\pi\) | |||||||
\(464\) | 6.24960 | 0.290130 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.92012 | 0.227920 | ||||||||
\(467\) | 17.5775 | 0.813389 | 0.406694 | − | 0.913564i | \(-0.366681\pi\) | ||||
0.406694 | + | 0.913564i | \(0.366681\pi\) | |||||||
\(468\) | 6.14058 | 0.283849 | ||||||||
\(469\) | 27.3279 | 1.26188 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.57908 | −0.118838 | ||||||||
\(472\) | 14.5583 | 0.670101 | ||||||||
\(473\) | 4.76196 | 0.218955 | ||||||||
\(474\) | 3.16135 | 0.145206 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.19049 | −0.0545660 | ||||||||
\(477\) | −18.6965 | −0.856053 | ||||||||
\(478\) | −2.98083 | −0.136340 | ||||||||
\(479\) | 22.7372 | 1.03889 | 0.519446 | − | 0.854504i | \(-0.326139\pi\) | ||||
0.519446 | + | 0.854504i | \(0.326139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0898462 | −0.00409664 | ||||||||
\(482\) | −20.0383 | −0.912722 | ||||||||
\(483\) | 22.3678 | 1.01777 | ||||||||
\(484\) | −10.0783 | −0.458104 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.3902 | 0.562030 | ||||||||
\(487\) | −22.1981 | −1.00589 | −0.502946 | − | 0.864318i | \(-0.667751\pi\) | ||||
−0.502946 | + | 0.864318i | \(0.667751\pi\) | |||||||
\(488\) | −7.53914 | −0.341281 | ||||||||
\(489\) | 11.1582 | 0.504589 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.9984 | −1.12816 | −0.564081 | − | 0.825719i | \(-0.690769\pi\) | ||||
−0.564081 | + | 0.825719i | \(0.690769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.55991 | 0.0702547 | ||||||||
\(494\) | 2.24960 | 0.101214 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.96006 | 0.132911 | ||||||||
\(497\) | 45.8786 | 2.05794 | ||||||||
\(498\) | −3.87859 | −0.173804 | ||||||||
\(499\) | 11.6574 | 0.521855 | 0.260928 | − | 0.965358i | \(-0.415972\pi\) | ||||
0.260928 | + | 0.965358i | \(0.415972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.74043 | 0.256463 | ||||||||
\(502\) | 14.8802 | 0.664135 | ||||||||
\(503\) | 11.7504 | 0.523924 | 0.261962 | − | 0.965078i | \(-0.415630\pi\) | ||||
0.261962 | + | 0.965078i | \(0.415630\pi\) | |||||||
\(504\) | −13.0192 | −0.579920 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.65896 | −0.384938 | ||||||||
\(507\) | 4.12819 | 0.183339 | ||||||||
\(508\) | 17.9585 | 0.796778 | ||||||||
\(509\) | 29.9569 | 1.32781 | 0.663907 | − | 0.747815i | \(-0.268897\pi\) | ||||
0.663907 | + | 0.747815i | \(0.268897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −57.5168 | −2.54439 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.97923 | 0.131536 | ||||||||
\(514\) | 11.0399 | 0.486951 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.57908 | −0.113538 | ||||||||
\(517\) | −9.11982 | −0.401089 | ||||||||
\(518\) | 0.190491 | 0.00836968 | ||||||||
\(519\) | −8.81788 | −0.387062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.1198 | −0.662411 | −0.331206 | − | 0.943559i | \(-0.607455\pi\) | ||||
−0.331206 | + | 0.943559i | \(0.607455\pi\) | |||||||
\(522\) | 17.0591 | 0.746657 | ||||||||
\(523\) | 15.6498 | 0.684316 | 0.342158 | − | 0.939642i | \(-0.388842\pi\) | ||||
0.342158 | + | 0.939642i | \(0.388842\pi\) | |||||||
\(524\) | −6.96006 | −0.304052 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.84025 | 0.167443 | ||||||||
\(527\) | 0.738835 | 0.0321842 | ||||||||
\(528\) | −0.499202 | −0.0217250 | ||||||||
\(529\) | 58.3455 | 2.53676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.7388 | 1.72452 | ||||||||
\(532\) | −4.76957 | −0.206787 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.12141 | 0.0918024 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.72963 | 0.247482 | ||||||||
\(537\) | −1.32028 | −0.0569741 | ||||||||
\(538\) | −23.1981 | −1.00014 | ||||||||
\(539\) | 15.1198 | 0.651257 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.2995 | −1.17370 | −0.586849 | − | 0.809697i | \(-0.699632\pi\) | ||||
−0.586849 | + | 0.809697i | \(0.699632\pi\) | |||||||
\(542\) | −23.9792 | −1.03000 | ||||||||
\(543\) | 2.01758 | 0.0865825 | ||||||||
\(544\) | −0.249601 | −0.0107016 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.57908 | 0.238763 | ||||||||
\(547\) | −33.9968 | −1.45360 | −0.726799 | − | 0.686850i | \(-0.758993\pi\) | ||||
−0.726799 | + | 0.686850i | \(0.758993\pi\) | |||||||
\(548\) | 7.80951 | 0.333606 | ||||||||
\(549\) | −20.5791 | −0.878294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.24960 | 0.266242 | ||||||||
\(552\) | 4.68969 | 0.199607 | ||||||||
\(553\) | −28.9984 | −1.23314 | ||||||||
\(554\) | −24.6590 | −1.04766 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.0383 | −0.680177 | ||||||||
\(557\) | 33.8786 | 1.43548 | 0.717741 | − | 0.696310i | \(-0.245176\pi\) | ||||
0.717741 | + | 0.696310i | \(0.245176\pi\) | |||||||
\(558\) | 8.07988 | 0.342048 | ||||||||
\(559\) | −11.1582 | −0.471940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.124602 | −0.00526068 | ||||||||
\(562\) | 18.9984 | 0.801399 | ||||||||
\(563\) | 32.2995 | 1.36126 | 0.680631 | − | 0.732626i | \(-0.261706\pi\) | ||||
0.680631 | + | 0.732626i | \(0.261706\pi\) | |||||||
\(564\) | 4.93929 | 0.207982 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29.0367 | −1.22051 | ||||||||
\(567\) | −31.6689 | −1.32997 | ||||||||
\(568\) | 9.61902 | 0.403605 | ||||||||
\(569\) | −6.73883 | −0.282507 | −0.141253 | − | 0.989973i | \(-0.545113\pi\) | ||||
−0.141253 | + | 0.989973i | \(0.545113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.4193 | 1.44040 | 0.720202 | − | 0.693764i | \(-0.244049\pi\) | ||||
0.720202 | + | 0.693764i | \(0.244049\pi\) | |||||||
\(572\) | −2.15975 | −0.0903039 | ||||||||
\(573\) | −1.07067 | −0.0447281 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.72963 | −0.113735 | ||||||||
\(577\) | 28.1773 | 1.17304 | 0.586519 | − | 0.809936i | \(-0.300498\pi\) | ||||
0.586519 | + | 0.809936i | \(0.300498\pi\) | |||||||
\(578\) | 16.9377 | 0.704515 | ||||||||
\(579\) | 4.39939 | 0.182832 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.5775 | 1.47600 | ||||||||
\(582\) | 9.57748 | 0.397000 | ||||||||
\(583\) | 6.57589 | 0.272346 | ||||||||
\(584\) | −12.0591 | −0.499010 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.24960 | −0.258169 | ||||||||
\(587\) | −34.6174 | −1.42881 | −0.714407 | − | 0.699730i | \(-0.753303\pi\) | ||||
−0.714407 | + | 0.699730i | \(0.753303\pi\) | |||||||
\(588\) | −8.18890 | −0.337704 | ||||||||
\(589\) | 2.96006 | 0.121967 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.23804 | −0.297733 | ||||||||
\(592\) | 0.0399387 | 0.00164147 | ||||||||
\(593\) | −3.99840 | −0.164195 | −0.0820974 | − | 0.996624i | \(-0.526162\pi\) | ||||
−0.0820974 | + | 0.996624i | \(0.526162\pi\) | |||||||
\(594\) | −2.86025 | −0.117357 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.41932 | −0.344869 | ||||||||
\(597\) | 4.75801 | 0.194732 | ||||||||
\(598\) | 20.2895 | 0.829701 | ||||||||
\(599\) | −42.5759 | −1.73960 | −0.869802 | − | 0.493401i | \(-0.835753\pi\) | ||||
−0.869802 | + | 0.493401i | \(0.835753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.4577 | −0.752904 | −0.376452 | − | 0.926436i | \(-0.622856\pi\) | ||||
−0.376452 | + | 0.926436i | \(0.622856\pi\) | |||||||
\(602\) | 23.6574 | 0.964202 | ||||||||
\(603\) | 15.6398 | 0.636901 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.88018 | 0.116999 | ||||||||
\(607\) | −12.5791 | −0.510569 | −0.255285 | − | 0.966866i | \(-0.582169\pi\) | ||||
−0.255285 | + | 0.966866i | \(0.582169\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 15.4992 | 0.628059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.3694 | 0.864514 | ||||||||
\(612\) | −0.681319 | −0.0275407 | ||||||||
\(613\) | −26.5759 | −1.07339 | −0.536695 | − | 0.843776i | \(-0.680327\pi\) | ||||
−0.536695 | + | 0.843776i | \(0.680327\pi\) | |||||||
\(614\) | −12.5391 | −0.506039 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.57908 | 0.184496 | ||||||||
\(617\) | −37.8386 | −1.52333 | −0.761663 | − | 0.647973i | \(-0.775617\pi\) | ||||
−0.761663 | + | 0.647973i | \(0.775617\pi\) | |||||||
\(618\) | −3.42092 | −0.137610 | ||||||||
\(619\) | 30.1566 | 1.21209 | 0.606047 | − | 0.795429i | \(-0.292754\pi\) | ||||
0.606047 | + | 0.795429i | \(0.292754\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.8702 | 1.07826 | ||||||||
\(622\) | −7.84785 | −0.314670 | ||||||||
\(623\) | −19.4593 | −0.779619 | ||||||||
\(624\) | 1.16972 | 0.0468264 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.9884 | −0.439186 | ||||||||
\(627\) | −0.499202 | −0.0199362 | ||||||||
\(628\) | 4.96006 | 0.197928 | ||||||||
\(629\) | 0.00996876 | 0.000397480 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4992 | −1.01511 | −0.507554 | − | 0.861620i | \(-0.669450\pi\) | ||||
−0.507554 | + | 0.861620i | \(0.669450\pi\) | |||||||
\(632\) | −6.07988 | −0.241845 | ||||||||
\(633\) | −8.58988 | −0.341417 | ||||||||
\(634\) | 21.5567 | 0.856127 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.56150 | −0.141223 | ||||||||
\(637\) | −35.4285 | −1.40373 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 26.2564 | 1.03869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.1965 | 1.54817 | 0.774084 | − | 0.633082i | \(-0.218211\pi\) | ||||
0.774084 | + | 0.633082i | \(0.218211\pi\) | |||||||
\(642\) | 7.75199 | 0.305947 | ||||||||
\(643\) | −36.3778 | −1.43460 | −0.717300 | − | 0.696764i | \(-0.754622\pi\) | ||||
−0.717300 | + | 0.696764i | \(0.754622\pi\) | |||||||
\(644\) | −43.0176 | −1.69513 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.249601 | −0.00982043 | ||||||||
\(647\) | −10.6897 | −0.420255 | −0.210128 | − | 0.977674i | \(-0.567388\pi\) | ||||
−0.210128 | + | 0.977674i | \(0.567388\pi\) | |||||||
\(648\) | −6.63979 | −0.260835 | ||||||||
\(649\) | −13.9769 | −0.548640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.34104 | 0.287718 | ||||||||
\(652\) | −21.4593 | −0.840410 | ||||||||
\(653\) | 36.0383 | 1.41029 | 0.705145 | − | 0.709063i | \(-0.250882\pi\) | ||||
0.705145 | + | 0.709063i | \(0.250882\pi\) | |||||||
\(654\) | 2.48003 | 0.0969769 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.9169 | −1.28421 | ||||||||
\(658\) | −45.3071 | −1.76626 | ||||||||
\(659\) | 17.1889 | 0.669584 | 0.334792 | − | 0.942292i | \(-0.391334\pi\) | ||||
0.334792 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.9054 | 1.90220 | 0.951099 | − | 0.308886i | \(-0.0999560\pi\) | ||||
0.951099 | + | 0.308886i | \(0.0999560\pi\) | |||||||
\(662\) | −33.4876 | −1.30153 | ||||||||
\(663\) | 0.291964 | 0.0113390 | ||||||||
\(664\) | 7.45926 | 0.289476 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.109018 | 0.00422436 | ||||||||
\(667\) | 56.3662 | 2.18251 | ||||||||
\(668\) | −11.0399 | −0.427148 | ||||||||
\(669\) | −4.70049 | −0.181731 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.23804 | 0.279421 | ||||||||
\(672\) | −2.48003 | −0.0956693 | ||||||||
\(673\) | −6.57908 | −0.253605 | −0.126802 | − | 0.991928i | \(-0.540471\pi\) | ||||
−0.126802 | + | 0.991928i | \(0.540471\pi\) | |||||||
\(674\) | −5.69890 | −0.219513 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.93929 | −0.305357 | ||||||||
\(677\) | 38.3087 | 1.47232 | 0.736162 | − | 0.676806i | \(-0.236636\pi\) | ||||
0.736162 | + | 0.676806i | \(0.236636\pi\) | |||||||
\(678\) | 3.11982 | 0.119816 | ||||||||
\(679\) | −87.8523 | −3.37146 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.182117 | −0.00697874 | ||||||||
\(682\) | −2.84184 | −0.108820 | ||||||||
\(683\) | −7.54074 | −0.288538 | −0.144269 | − | 0.989538i | \(-0.546083\pi\) | ||||
−0.144269 | + | 0.989538i | \(0.546083\pi\) | |||||||
\(684\) | −2.72963 | −0.104370 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 41.7280 | 1.59318 | ||||||||
\(687\) | 4.20129 | 0.160289 | ||||||||
\(688\) | 4.96006 | 0.189101 | ||||||||
\(689\) | −15.4085 | −0.587018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.4193 | 1.08112 | 0.540561 | − | 0.841305i | \(-0.318212\pi\) | ||||
0.540561 | + | 0.841305i | \(0.318212\pi\) | |||||||
\(692\) | 16.9585 | 0.644664 | ||||||||
\(693\) | 12.4992 | 0.474805 | ||||||||
\(694\) | 0.239632 | 0.00909632 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.24960 | 0.123176 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 17.2380 | 0.652469 | ||||||||
\(699\) | 2.55831 | 0.0967643 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.2596 | −0.916271 | −0.458136 | − | 0.888882i | \(-0.651483\pi\) | ||||
−0.458136 | + | 0.888882i | \(0.651483\pi\) | |||||||
\(702\) | 6.70209 | 0.252954 | ||||||||
\(703\) | 0.0399387 | 0.00150632 | ||||||||
\(704\) | 0.960061 | 0.0361837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.7280 | 1.30701 | ||||||||
\(707\) | −26.4193 | −0.993601 | ||||||||
\(708\) | 7.56988 | 0.284493 | ||||||||
\(709\) | 21.7372 | 0.816359 | 0.408180 | − | 0.912902i | \(-0.366164\pi\) | ||||
0.408180 | + | 0.912902i | \(0.366164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.5958 | −0.622392 | ||||||||
\(712\) | −4.07988 | −0.152900 | ||||||||
\(713\) | 26.6973 | 0.999822 | ||||||||
\(714\) | −0.619019 | −0.0231662 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.53914 | 0.0948922 | ||||||||
\(717\) | −1.54994 | −0.0578835 | ||||||||
\(718\) | −26.6689 | −0.995275 | ||||||||
\(719\) | −48.9361 | −1.82501 | −0.912504 | − | 0.409067i | \(-0.865854\pi\) | ||||
−0.912504 | + | 0.409067i | \(0.865854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.3794 | 1.16863 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −10.4193 | −0.387499 | ||||||||
\(724\) | −3.88018 | −0.144206 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.24040 | −0.194489 | ||||||||
\(727\) | −4.29874 | −0.159432 | −0.0797158 | − | 0.996818i | \(-0.525401\pi\) | ||||
−0.0797158 | + | 0.996818i | \(0.525401\pi\) | |||||||
\(728\) | −10.7296 | −0.397667 | ||||||||
\(729\) | −13.4768 | −0.499142 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.23804 | 0.0457905 | ||||||||
\(732\) | −3.92012 | −0.144892 | ||||||||
\(733\) | −12.0415 | −0.444764 | −0.222382 | − | 0.974960i | \(-0.571383\pi\) | ||||
−0.222382 | + | 0.974960i | \(0.571383\pi\) | |||||||
\(734\) | 15.2380 | 0.562446 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.01917 | −0.332451 | ||||||||
\(737\) | −5.50080 | −0.202624 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.61742 | 0.243426 | 0.121713 | − | 0.992565i | \(-0.461161\pi\) | ||||
0.121713 | + | 0.992565i | \(0.461161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.16972 | 0.0429709 | ||||||||
\(742\) | 32.6689 | 1.19931 | ||||||||
\(743\) | −47.6158 | −1.74686 | −0.873428 | − | 0.486954i | \(-0.838108\pi\) | ||||
−0.873428 | + | 0.486954i | \(0.838108\pi\) | |||||||
\(744\) | 1.53914 | 0.0564277 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.6382 | 0.975293 | ||||||||
\(747\) | 20.3610 | 0.744972 | ||||||||
\(748\) | 0.239632 | 0.00876183 | ||||||||
\(749\) | −71.1074 | −2.59821 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6574 | −0.936250 | −0.468125 | − | 0.883662i | \(-0.655070\pi\) | ||||
−0.468125 | + | 0.883662i | \(0.655070\pi\) | |||||||
\(752\) | −9.49920 | −0.346400 | ||||||||
\(753\) | 7.73724 | 0.281961 | ||||||||
\(754\) | 14.0591 | 0.512003 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14.2097 | −0.516800 | ||||||||
\(757\) | 8.83865 | 0.321246 | 0.160623 | − | 0.987016i | \(-0.448650\pi\) | ||||
0.160623 | + | 0.987016i | \(0.448650\pi\) | |||||||
\(758\) | −11.9693 | −0.434743 | ||||||||
\(759\) | −4.50239 | −0.163426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.40776 | −0.341031 | −0.170516 | − | 0.985355i | \(-0.554543\pi\) | ||||
−0.170516 | + | 0.985355i | \(0.554543\pi\) | |||||||
\(762\) | 9.33785 | 0.338275 | ||||||||
\(763\) | −22.7488 | −0.823562 | ||||||||
\(764\) | 2.05911 | 0.0744960 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.84025 | 0.355543 | ||||||||
\(767\) | 32.7504 | 1.18255 | ||||||||
\(768\) | −0.519969 | −0.0187628 | ||||||||
\(769\) | 7.32788 | 0.264250 | 0.132125 | − | 0.991233i | \(-0.457820\pi\) | ||||
0.132125 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.74043 | 0.206737 | ||||||||
\(772\) | −8.46086 | −0.304513 | ||||||||
\(773\) | 54.4369 | 1.95796 | 0.978980 | − | 0.203958i | \(-0.0653806\pi\) | ||||
0.978980 | + | 0.203958i | \(0.0653806\pi\) | |||||||
\(774\) | 13.5391 | 0.486654 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.4193 | −0.661215 | ||||||||
\(777\) | 0.0990493 | 0.00355337 | ||||||||
\(778\) | 8.65896 | 0.310439 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.23485 | −0.330449 | ||||||||
\(782\) | −2.25120 | −0.0805026 | ||||||||
\(783\) | 18.6190 | 0.665389 | ||||||||
\(784\) | 15.7488 | 0.562457 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.61902 | −0.129086 | ||||||||
\(787\) | −27.6705 | −0.986348 | −0.493174 | − | 0.869931i | \(-0.664163\pi\) | ||||
−0.493174 | + | 0.869931i | \(0.664163\pi\) | |||||||
\(788\) | 13.9201 | 0.495884 | ||||||||
\(789\) | 1.99681 | 0.0710883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.6174 | −1.01752 | ||||||||
\(792\) | 2.62061 | 0.0931195 | ||||||||
\(793\) | −16.9601 | −0.602269 | ||||||||
\(794\) | −28.9984 | −1.02911 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.15055 | −0.324333 | ||||||||
\(797\) | 21.5906 | 0.764780 | 0.382390 | − | 0.924001i | \(-0.375101\pi\) | ||||
0.382390 | + | 0.924001i | \(0.375101\pi\) | |||||||
\(798\) | −2.48003 | −0.0877921 | ||||||||
\(799\) | −2.37101 | −0.0838804 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1366 | −0.393491 | ||||||||
\(802\) | −22.6174 | −0.798649 | ||||||||
\(803\) | 11.5775 | 0.408561 | ||||||||
\(804\) | 2.97923 | 0.105069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.65896 | 0.234552 | ||||||||
\(807\) | −12.0623 | −0.424613 | ||||||||
\(808\) | −5.53914 | −0.194866 | ||||||||
\(809\) | 9.72963 | 0.342076 | 0.171038 | − | 0.985264i | \(-0.445288\pi\) | ||||
0.171038 | + | 0.985264i | \(0.445288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.7280 | −1.35993 | −0.679963 | − | 0.733247i | \(-0.738004\pi\) | ||||
−0.679963 | + | 0.733247i | \(0.738004\pi\) | |||||||
\(812\) | −29.8079 | −1.04605 | ||||||||
\(813\) | −12.4685 | −0.437288 | ||||||||
\(814\) | −0.0383436 | −0.00134394 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.129785 | −0.00454338 | ||||||||
\(817\) | 4.96006 | 0.173531 | ||||||||
\(818\) | −5.34104 | −0.186745 | ||||||||
\(819\) | −29.2879 | −1.02340 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.2780 | −1.05671 | −0.528354 | − | 0.849024i | \(-0.677191\pi\) | ||||
−0.528354 | + | 0.849024i | \(0.677191\pi\) | |||||||
\(822\) | 4.06071 | 0.141633 | ||||||||
\(823\) | −7.93770 | −0.276691 | −0.138345 | − | 0.990384i | \(-0.544178\pi\) | ||||
−0.138345 | + | 0.990384i | \(0.544178\pi\) | |||||||
\(824\) | 6.57908 | 0.229193 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69.4369 | −2.41602 | ||||||||
\(827\) | 30.2496 | 1.05188 | 0.525941 | − | 0.850521i | \(-0.323713\pi\) | ||||
0.525941 | + | 0.850521i | \(0.323713\pi\) | |||||||
\(828\) | −24.6190 | −0.855570 | ||||||||
\(829\) | −40.6765 | −1.41275 | −0.706377 | − | 0.707836i | \(-0.749672\pi\) | ||||
−0.706377 | + | 0.707836i | \(0.749672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.8219 | −0.444787 | ||||||||
\(832\) | −2.24960 | −0.0779909 | ||||||||
\(833\) | 3.93092 | 0.136198 | ||||||||
\(834\) | −8.33945 | −0.288771 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.960061 | 0.0332044 | ||||||||
\(837\) | 8.81871 | 0.304819 | ||||||||
\(838\) | 22.1566 | 0.765386 | ||||||||
\(839\) | 45.9553 | 1.58655 | 0.793276 | − | 0.608862i | \(-0.208374\pi\) | ||||
0.793276 | + | 0.608862i | \(0.208374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0575 | 0.346811 | ||||||||
\(842\) | −29.2787 | −1.00901 | ||||||||
\(843\) | 9.87859 | 0.340237 | ||||||||
\(844\) | 16.5200 | 0.568641 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.9293 | −0.891469 | ||||||||
\(847\) | 48.0691 | 1.65167 | ||||||||
\(848\) | 6.84945 | 0.235211 | ||||||||
\(849\) | −15.0982 | −0.518170 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.360214 | 0.0123480 | ||||||||
\(852\) | 5.00160 | 0.171352 | ||||||||
\(853\) | 17.2196 | 0.589589 | 0.294794 | − | 0.955561i | \(-0.404749\pi\) | ||||
0.294794 | + | 0.955561i | \(0.404749\pi\) | |||||||
\(854\) | 35.9585 | 1.23047 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9086 | −0.509564 | ||||||||
\(857\) | 17.2995 | 0.590940 | 0.295470 | − | 0.955352i | \(-0.404524\pi\) | ||||
0.295470 | + | 0.955352i | \(0.404524\pi\) | |||||||
\(858\) | −1.12301 | −0.0383388 | ||||||||
\(859\) | 17.6190 | 0.601153 | 0.300577 | − | 0.953758i | \(-0.402821\pi\) | ||||
0.300577 | + | 0.953758i | \(0.402821\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.3794 | −0.728185 | ||||||||
\(863\) | −4.07988 | −0.138881 | −0.0694403 | − | 0.997586i | \(-0.522121\pi\) | ||||
−0.0694403 | + | 0.997586i | \(0.522121\pi\) | |||||||
\(864\) | −2.97923 | −0.101356 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.1182 | 1.22735 | ||||||||
\(867\) | 8.80708 | 0.299104 | ||||||||
\(868\) | −14.1182 | −0.479204 | ||||||||
\(869\) | 5.83705 | 0.198009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8894 | 0.436740 | ||||||||
\(872\) | −4.76957 | −0.161518 | ||||||||
\(873\) | −50.2780 | −1.70165 | ||||||||
\(874\) | −9.01917 | −0.305078 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.27037 | −0.211856 | ||||||||
\(877\) | 25.2787 | 0.853602 | 0.426801 | − | 0.904345i | \(-0.359640\pi\) | ||||
0.426801 | + | 0.904345i | \(0.359640\pi\) | |||||||
\(878\) | −20.9984 | −0.708662 | ||||||||
\(879\) | −3.24960 | −0.109606 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.0814726 | −0.00274488 | −0.00137244 | − | 0.999999i | \(-0.500437\pi\) | ||||
−0.00137244 | + | 0.999999i | \(0.500437\pi\) | |||||||
\(882\) | 42.9884 | 1.44750 | ||||||||
\(883\) | 19.3410 | 0.650878 | 0.325439 | − | 0.945563i | \(-0.394488\pi\) | ||||
0.325439 | + | 0.945563i | \(0.394488\pi\) | |||||||
\(884\) | −0.561503 | −0.0188854 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.4976 | 1.05818 | ||||||||
\(887\) | 5.53914 | 0.185986 | 0.0929931 | − | 0.995667i | \(-0.470357\pi\) | ||||
0.0929931 | + | 0.995667i | \(0.470357\pi\) | |||||||
\(888\) | 0.0207669 | 0.000696892 0 | ||||||||
\(889\) | −85.6542 | −2.87275 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.37460 | 0.213557 | ||||||||
\(892\) | 9.03994 | 0.302680 | ||||||||
\(893\) | −9.49920 | −0.317879 | ||||||||
\(894\) | −4.37779 | −0.146415 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.76957 | 0.159340 | ||||||||
\(897\) | 10.5499 | 0.352252 | ||||||||
\(898\) | −18.9601 | −0.632705 | ||||||||
\(899\) | 18.4992 | 0.616983 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.70963 | 0.0569561 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.3011 | 0.409355 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.3994 | 0.345497 | ||||||||
\(907\) | 10.8111 | 0.358977 | 0.179488 | − | 0.983760i | \(-0.442556\pi\) | ||||
0.179488 | + | 0.983760i | \(0.442556\pi\) | |||||||
\(908\) | 0.350246 | 0.0116233 | ||||||||
\(909\) | −15.1198 | −0.501493 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.1166 | 1.16347 | 0.581733 | − | 0.813380i | \(-0.302375\pi\) | ||||
0.581733 | + | 0.813380i | \(0.302375\pi\) | |||||||
\(912\) | −0.519969 | −0.0172179 | ||||||||
\(913\) | −7.16135 | −0.237006 | ||||||||
\(914\) | 6.32948 | 0.209361 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.07988 | −0.266967 | ||||||||
\(917\) | 33.1965 | 1.09625 | ||||||||
\(918\) | −0.743620 | −0.0245431 | ||||||||
\(919\) | 30.8287 | 1.01694 | 0.508472 | − | 0.861078i | \(-0.330210\pi\) | ||||
0.508472 | + | 0.861078i | \(0.330210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.51997 | −0.214840 | ||||||||
\(922\) | 6.49920 | 0.214040 | ||||||||
\(923\) | 21.6390 | 0.712255 | ||||||||
\(924\) | 2.38098 | 0.0783285 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28.4177 | −0.933865 | ||||||||
\(927\) | 17.9585 | 0.589833 | ||||||||
\(928\) | −6.24960 | −0.205153 | ||||||||
\(929\) | −45.0575 | −1.47829 | −0.739145 | − | 0.673547i | \(-0.764770\pi\) | ||||
−0.739145 | + | 0.673547i | \(0.764770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.7488 | 0.516146 | ||||||||
\(932\) | −4.92012 | −0.161164 | ||||||||
\(933\) | −4.08064 | −0.133594 | ||||||||
\(934\) | −17.5775 | −0.575153 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.14058 | −0.200711 | ||||||||
\(937\) | −22.2464 | −0.726759 | −0.363379 | − | 0.931641i | \(-0.618377\pi\) | ||||
−0.363379 | + | 0.931641i | \(0.618377\pi\) | |||||||
\(938\) | −27.3279 | −0.892287 | ||||||||
\(939\) | −5.71365 | −0.186458 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.9277 | −1.75799 | −0.878997 | − | 0.476828i | \(-0.841787\pi\) | ||||
−0.878997 | + | 0.476828i | \(0.841787\pi\) | |||||||
\(942\) | 2.57908 | 0.0840310 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −14.5583 | −0.473833 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.76196 | −0.154825 | ||||||||
\(947\) | 4.76196 | 0.154743 | 0.0773715 | − | 0.997002i | \(-0.475347\pi\) | ||||
0.0773715 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(948\) | −3.16135 | −0.102676 | ||||||||
\(949\) | −27.1282 | −0.880618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2088 | 0.363471 | ||||||||
\(952\) | 1.19049 | 0.0385840 | ||||||||
\(953\) | −4.37779 | −0.141811 | −0.0709053 | − | 0.997483i | \(-0.522589\pi\) | ||||
−0.0709053 | + | 0.997483i | \(0.522589\pi\) | |||||||
\(954\) | 18.6965 | 0.605321 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.98083 | 0.0964069 | ||||||||
\(957\) | −3.11982 | −0.100849 | ||||||||
\(958\) | −22.7372 | −0.734607 | ||||||||
\(959\) | −37.2480 | −1.20280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2380 | −0.717356 | ||||||||
\(962\) | 0.0898462 | 0.00289676 | ||||||||
\(963\) | −40.6949 | −1.31137 | ||||||||
\(964\) | 20.0383 | 0.645392 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −22.3678 | −0.719673 | ||||||||
\(967\) | 13.1582 | 0.423138 | 0.211569 | − | 0.977363i | \(-0.432143\pi\) | ||||
0.211569 | + | 0.977363i | \(0.432143\pi\) | |||||||
\(968\) | 10.0783 | 0.323928 | ||||||||
\(969\) | −0.129785 | −0.00416929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9201 | 0.831816 | 0.415908 | − | 0.909407i | \(-0.363464\pi\) | ||||
0.415908 | + | 0.909407i | \(0.363464\pi\) | |||||||
\(972\) | −12.3902 | −0.397415 | ||||||||
\(973\) | 76.4960 | 2.45235 | ||||||||
\(974\) | 22.1981 | 0.711273 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.53914 | 0.241322 | ||||||||
\(977\) | −31.2764 | −1.00062 | −0.500310 | − | 0.865846i | \(-0.666781\pi\) | ||||
−0.500310 | + | 0.865846i | \(0.666781\pi\) | |||||||
\(978\) | −11.1582 | −0.356799 | ||||||||
\(979\) | 3.91693 | 0.125186 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0192 | −0.415670 | ||||||||
\(982\) | 24.9984 | 0.797731 | ||||||||
\(983\) | −26.2364 | −0.836813 | −0.418406 | − | 0.908260i | \(-0.637411\pi\) | ||||
−0.418406 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.55991 | −0.0496776 | ||||||||
\(987\) | −23.5583 | −0.749869 | ||||||||
\(988\) | −2.24960 | −0.0715693 | ||||||||
\(989\) | 44.7356 | 1.42251 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.2764 | 1.24766 | 0.623828 | − | 0.781562i | \(-0.285577\pi\) | ||||
0.623828 | + | 0.781562i | \(0.285577\pi\) | |||||||
\(992\) | −2.96006 | −0.0939820 | ||||||||
\(993\) | −17.4125 | −0.552570 | ||||||||
\(994\) | −45.8786 | −1.45518 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.87859 | 0.122898 | ||||||||
\(997\) | −14.4609 | −0.457980 | −0.228990 | − | 0.973429i | \(-0.573542\pi\) | ||||
−0.228990 | + | 0.973429i | \(0.573542\pi\) | |||||||
\(998\) | −11.6574 | −0.369007 | ||||||||
\(999\) | 0.118987 | 0.00376458 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 950.2.a.j.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 8550.2.a.cp.1.1 | 3 | |||
4.3 | odd | 2 | 7600.2.a.bz.1.2 | 3 | |||
5.2 | odd | 4 | 950.2.b.h.799.2 | 6 | |||
5.3 | odd | 4 | 950.2.b.h.799.5 | 6 | |||
5.4 | even | 2 | 950.2.a.l.1.2 | yes | 3 | ||
15.14 | odd | 2 | 8550.2.a.ci.1.3 | 3 | |||
20.19 | odd | 2 | 7600.2.a.bk.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.j.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
950.2.a.l.1.2 | yes | 3 | 5.4 | even | 2 | ||
950.2.b.h.799.2 | 6 | 5.2 | odd | 4 | |||
950.2.b.h.799.5 | 6 | 5.3 | odd | 4 | |||
7600.2.a.bk.1.2 | 3 | 20.19 | odd | 2 | |||
7600.2.a.bz.1.2 | 3 | 4.3 | odd | 2 | |||
8550.2.a.ci.1.3 | 3 | 15.14 | odd | 2 | |||
8550.2.a.cp.1.1 | 3 | 3.2 | odd | 2 |